Fluctuation theory for Lévy processes with completely monotone jumps

Keywords

Mathematics, Infimum and supremum, Monotonic function, Monotone polygon, Factorization

References

• Introductory Lectures on Fluctuations of Lévy Processes with ApplicationsAndreas E. Kyprianou — 2006
• Potential Analysis of Stable Processes and its ExtensionsKrzysztof Bogdan, Tomasz Byczkowski, Tadeusz Kulczycki — 2009
• On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motionS. Fotopoulos, Venkata K. Jandhyala, Jun Wang — 2015
• Information Theory, Inference, and Learning AlgorithmsYuhong Yang — 2005
• On Harnack Inequality and Hölder Regularity for Isotropic Unimodal Lévy ProcessesTomasz Grzywny — 2013
• Spectral expansions of non-self-adjoint generalized Laguerre semigroupsPierre Patie, Mladen Savov — 2015
• Spectral properties of the Cauchy process on half‐line and intervalTadeusz Kulczycki, Mateusz Kwaśnicki, Jacek Małecki — 2009
• Bernstein Functions: Theory and ApplicationsRené L. Schilling, Renming Song, Zoran Vondraček — 2010
• Lévy processes and infinitely divisible distributions健一 佐藤 — 2013
• Lévy Processes and Stochastic CalculusDavid Applebaum — 2004
• Intrinsic compound kernel estimates for the transition probability density of a L\'evy type processes and their applicationsVictoria Knopova, Aleksei Kulik — 2013
• Deep factorisation of the stable processAndreas E. Kyprianou — 2015
• On the supremum of the spectrally negative stable process with driftGuillaume Coqueret — 2015
• Wiener–Hopf factorization and distribution of extrema for a family of Lévy processesAlexey Kuznetsov — 2010
• Wiener–Hopf Factorization of Diffusions and Lévy ProcessesL. C. G. Rogers — 1983
• Maxima of sums of random variables and suprema of stable processesΝ. H. Bingham — 1973
• On a Fluctuation Identity for Multidimensional L\'evy ProcessesYozo Tamura, Hiroshi Tanaka — 2002
• Density and tails of unimodal convolution semigroupsKrzysztof Bogdan, Tomasz Grzywny, Michał Ryznar — 2013
• First passage times for subordinate Brownian motionsMateusz Kwaśnicki, Jacek Małecki, Michał Ryznar — 2011
• Boundary Harnack Principle and Martin Boundary at Infinity for Subordinate Brownian MotionsPanki Kim, Renming Song, Zoran Vondraček — 2012

Cited by

• A new class of bell-shaped functionsMateusz Kwaśnicki — 2017
• Harmonic extension technique for non-symmetric operators with completely monotone kernelsMateusz Kwaśnicki — 2019
• Characterisation of the class of bell-shaped functionsMateusz Kwaśnicki, Thomas Simon — 2019
• Spectral theory for one-dimensional (non-symmetric) stable processes killed upon hitting the originJacek Mucha — 2019
• Boundary traces of shift-invariant diffusions in half-planeMateusz Kwaśnicki — 2019
• Poisson kernels on the half‐plane are bell‐shapedMateusz Kwaśnicki — 2025

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• Controllability and qualitative properties of the solutions to SPDEs driven by boundary Lévy noiseErika Hausenblas, Paul André Razafimandimby — 2012
• Sample Path Properties of Volterra ProcessesLeonid Mytnik, Eyal Neuman — 2011
• Continuity and Boundedness of Infinitely Divisible Processes: A Poisson Point Process ApproachMichael B. Marcus, J. Rosiński — 2005